Levi tengsizligi uchun A.N. Kolmogorov teoremalari
DOI:
https://doi.org/10.5281/zenodo.15509901Ключевые слова:
Lévy tengsizligi, ehtimollik nazariyasi, tasodifiy miqdorlar, statistik tahlil, Kolmogorov tengsizligi, stoxastik jarayonlar.Аннотация
Ushbu maqolada Lévy tengsizligining ayrim umumlashmalari hamda ularning xossalari ko‘rib chiqiladi.
Tadqiqot davomida O. I. Klyosov, A. N. Kolmogorov va P. Lévy tomonidan keltirilgan tengsizliklarga asoslangan holda d>1
holati uchun yangi natijalar hosil qilinadi. Shuningdek, Lévy tengsizligining ba’zi xususiyatlari keltirilib, ularning matematik
isboti taqdim etilgan. Ushbu natijalar ehtimollik nazariyasi va statistik tahlil sohalarida muhim ahamiyat kasb etadi hamda
tasodifiy jarayonlarni o‘rganishda samarali vosita sifatida qo‘llanishi mumkin
Библиографические ссылки
P. Levy, “Probability Theory and Applications,” Springer, 1954.
A.N. Kolmogorov, “Foundations of the Theory of Probability,” Chelsea Publishing Company, 1956.
O.I. Klyosov, “Modern Developments in Probability Theory,” Moscow, 2001.
J. Neveu, “Mathematical Foundations of Probability,” Holden-Day, 1965.
Feller, W., “An Introduction to Probability Theory and Its Applications,” Vol. 2, Wiley, 1971.
William Feller. An Introduction to Probability Theory and Its Applications. – Wiley, 1950.
I.A. Ibragimov, Yu.V. Linnik. Nezavisimye i odnorodno raspredelennye velichiny. – M.: Nauka, 1965.
R. Durrett. Probability: Theory and Examples. – Cambridge University Press, 1996.
L. Breiman. Probability. – SIAM, 1992.
S.R.S. Varadhan. Large Deviations and Applications. – SIAM, 1984.
V.V. Petrov. Limit Theorems of Probability Theory: Sequences of Independent Random Variables. – Oxford University
Press, 1995.
B.V. Gnedenko, A.N. Kolmogorov. Limit Distributions for Sums of Independent Random Variables. – Addison-Wesley,
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